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4 x + y CANNOT be

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by sanju09 » Tue Nov 15, 2011 3:48 am
If x and y are integers and 2 x - y = 11, then 4 x + y CANNOT be
(A) -5
(B) 1
(C) 13
(D) 17
(E) 55
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by neelgandham » Tue Nov 15, 2011 3:50 am
If x and y are integers and 2 x - y = 11, then 4 x + y cannot be

2x -y = 11
4x -2y =22
4x +y = 22+3y

(A) -5 = 22+3y => 3y = -27 possible!
(B) 1 = 22+3y => 3y = -21 possible!
(C) 13 = 22+3y => 3y = -9 possible!
(D) 17 = 22+3y => 3y = -5 NOT possible!
(E) 55 = 22+3y => 3y = 33 possible

IMO D[spoiler][/spoiler]
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by shankar.ashwin » Tue Nov 15, 2011 4:01 am
2 x - y = 11
4 x + y = A (A- some number)

Adding, we have 6x = 11+A (or) 11+(answer choice) should be multiple of 6.

A,B,C and E when added with 11 are multiples of 6. D isn't.
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by sanju09 » Tue Nov 15, 2011 4:06 am
neelgandham wrote:If x and y are integers and 2 x - y = 11, then 4 x + y cannot be

2x -y = 11
4x -2y =22
4x +y = 22+3y

(A) -5 = 22+3y => 3y = -27 possible!
(B) 1 = 22+3y => 3y = -21 possible!
(C) 13 = 22+3y => 3y = -9 possible!
(D) 17 = 22+3y => 3y = -5 NOT possible!
(E) 55 = 22+3y => 3y = 33 possible

IMO D[spoiler][/spoiler]
Excellent!! But why do we need to check beyond (D)?
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by neelgandham » Tue Nov 15, 2011 4:10 am
sanju09 wrote:Excellent!! But why do we need to check beyond (D)?
I have done it just for the benefit of the readers(fellow BTGians). On the D-Day, I would have stopped it at D right away.
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by sanju09 » Tue Nov 15, 2011 4:43 am
neelgandham wrote:
sanju09 wrote:Excellent!! But why do we need to check beyond (D)?
I have done it just for the benefit of the readers(fellow BTGians). On the D-Day, I would have stopped it at D right away.
right
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